Incremental Network Design with Minimum Spanning Trees

Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where $w(X_t)$ is the weight of a minimum spanning tree $X_t$ for the subgraph $(V,E_0\cup\{e'_1,\ldots,e'_t\})$ and $T=\lvert E\setminus E_0\rvert$. We prove that this problem can be solved by a greedy algorithm.Comment: 9 pages, minor revision based on reviewer comment

An efficient implementation of local search algorithms for constrained routing problems

We investigate the implementation of local search algorithms for routing problems with various side constraints such as time windows on vertices and precedence relations between vertices. The algorithms are based on the k-exchange concept. In the case of unconstrained routing problems, a single k-exchange can obviously be processed in constant time. In the presence of side constraints feasibility problems arise. Testing the feasibility of a single solution requires an amount of time that is linear in the number of vertices. We show how this effort can, on the average, still be reduced to a constant

Time Slot Management in Attended Home Delivery

Many e-tailers providing attended home delivery, especially e-grocers, offer narrow delivery time slots to ensure satisfactory customer service. The choice of delivery time slots has to balance marketing and operational considerations, which results in a complex planning problem. We study the problem of selecting the set of time slots to offer in each of the zip codes in a service region. The selection needs to facilitate cost-effective delivery routes, but also needs to ensure an acceptable level of service to the customer. We present two fully-automated approaches that are capable of producing high-quality delivery time slot offerings in a reasonable amount of time. Computational experiments reveal the value of these approaches and the impact of the environment on the underlying trade-offs.integer programming;vehicle routing;continuous approximation;e-grocery;home delivery;time slots

A reclaimer scheduling problem arising in coal stockyard management

We study a number of variants of an abstract scheduling problem inspired by the scheduling of reclaimers in the stockyard of a coal export terminal. We analyze the complexity of each of the variants, providing complexity proofs for some and polynomial algorithms for others. For one, especially interesting variant, we also develop a constant factor approximation algorithm.Comment: 26 page